AUGUSTA, Maine — A consulting group hired by the state to study Medicaid expansion, among other topics, defended its initial report Tuesday against claims from a national health care organization that its math didn’t add up.

Crucial to that calculation is the projected contribution of the federal government, known as the “federal medical assistance percentage,” or FMAP. While expansion includes a 100 percent federal funding level for those low-income Mainers made newly eligible for the program, traditional populations and administrative costs will continue to be shared by the state and federal government.

According to a review of the report by Health Management Associates, a national consulting firm focused on health care programs for the poor, especially Medicaid, the numbers didn’t add up.

Health Management Associates’ Kathy Gifford — a former state Medicaid director in Indiana and co-author of the annual Medicaid Budget Survey Report for the Kaiser Foundation — wrote in a memo to the AARP that, according to her calculations, the Alexander Group used different numbers than it had claimed.

A lower federal match would naturally result in increased cost for the state.

The Alexander Group wrote that it used a range of different FMAP predictions for different populations covered by Medicaid, none of which fell below 61.55 percent traditional Medicaid match rate estimated for 2014.

“According to my calculations, however, a 60 percent FMAP rate was used instead, overstating the baseline costs over the 10-year period by $575 million,” Gifford wrote. “… It would be worth asking for additional detail for these calculations to determine if the overall federal share has been understated.”

Gifford wrote that the error appeared in the Alexander Groups’ baseline projection — that is, the expected growth in Medicaid costs if the state did not expand coverage. She said she could not determine whether a similar numbers switch was employed in the cost projections if Maine did expand the program.

Gifford based her review on simple calculations: The Alexander Group provided estimates of enrollment growth and state and federal spending for each year of the 10-year projection. She simply calculated the percentage of the total cost borne by each side.

Eric Randolph, an analyst with the Alexander Group who helped craft the report, said Tuesday that Gifford oversimplified the calculation, and that there was no such error.

Randolph said that because different areas of Medicaid spending receive different levels of federal funding, you can’t distill a match rate down to a single number.

“I’m kind of surprised she did it that way,” he said. “She should know better that you can’t calculate it that way.”

However, none of the estimated match rates identified by the Alexander Group in its report dipped below the 61.55 percent traditional Medicaid match rate projected for 2014. That left Gifford puzzled by how the average federal match across all categories could be 60 percent.

Murray Blitzer, another member of the Alexander Group, suggested Tuesday that the figures in the study included not just Medicaid spending, but also medical services paid for with state dollars only.

“If you look at the baseline, it’s coming off the state spending occurring in MaineCare and other related services,” he said. “Most Medicaid programs in the states, it’s a combination of Medicaid and some assistance that’s state-only.”

It was unclear exactly what state-funded services were included — or why they were included at all. Those services would not necessarily grow along with Medicaid expansion.

“If he’s including non-Medicaid costs in there, that would drive [the average match rate] down, I guess,” Gifford said. “But you’d have to say that if it’s a non-Medicaid program, why is it in there? A state-only program isn’t going to grow unless appropriations grow. Those aren’t entitlements.”

Efforts to reach Randolph and Blitzer for additional comment Tuesday were unsuccessful.

Gifford also raised concerns that had been voiced by other groups since the study was released on Jan. 10, namely that the report did not include any analysis of possible savings associated with Medicaid expansion, nor the economic impact of billions of federal dollars flowing into the state.

The Alexander Group has said those questions were outside the scope of its study.

Rep. Drew Gattine, D-Westbrook, sits on the Legislature’s Health and Human Services Committee, which on Wednesday will hold work sessions on two bills that would expand Medicaid in Maine, both of which are opposed by Republican lawmakers and Gov. Paul LePage, who cite the Alexander Group study in saying expansion would be too costly.

On Tuesday, Gattine said questions surrounding the report could easily have been addressed if the group had shown its work. He said questions about the FMAP rate were similar to those asked about the Alexander Group’s prediction that the number of Mainers living under the poverty line would grow 31.5 percent over 10 years. That prediction is a crucial factor driving up the cost of expansion outlined in the report.

“What they should do is show us their math, show us their formula,” he said. “It’s similar to the issue around the poverty rate. If they want to defend what they’re saying they used, then walk us through the math.”